Refer to all four items in Table 6.17.

a. Generalize the symmetry model, so that the cell probability is identical for all cells with the same set of response outcomes; that is, hijk is identical for all permutations of the subscript. Fit this complete symmetry model, and interpret. (Hint: Fit a model with a factor that has a different level for each distinct combination of the four indices.)

b. Fit a generalized quasi-symmetry model by using different main effect fac- tors for the four items. Test homogeneity of the four margins by comparing the fits of the complete symmetry and quasi-symmetry models. Interpret.

c. Fit a generalized ordinal quasi-symmetry model by adding a quantitative main effect term for each margin to the complete symmetry model. Use this model to test marginal homogeneity in a way that uses the ordering.